See the standard disclaimers. This is an exercise in fun more than analysis, although hopefully there's a touch of the latter or you're just wasting your time.

AL EAST

1. Boston

2. New York (wildcard)

3. Toronto (wildcard)

4. Baltimore

5. Tampa Bay

Picking the Red Sox is something of a tradition in this space. I don’t do it on purpose, it’s just that my “model” (such as it is) has tended to pick them consistently. This year it’s a virtual tie with the Yankees; some projections agree with that, but others (notably PECOTA) see a huge advantage for the latter. The Yankees arguably were more impressive last season given their component statistics, and yet Boston’s offense should bounce back, their starting pitching should be better, their bullpen could benefit from some healthy pieces coming back...and if Aaron Judge and Giancarlo Stanton combine for even ninety homers the takes will be hot. The top-heaviness of the AL, with four teams that really stand out, leaves a team like the Blue Jays a stealthy wildcard contender. Incidentally, I have them +9 runs on both offense and defense. The Orioles added enough late and the Rays subtracted enough to make me flip-flop their places, but it would be surprising if either gets into this race.

AL CENTRAL

1. Cleveland

2. Minnesota

3. Kansas City

4. Detroit

5. Chicago

As a partisan am I always queasy about picking the Indians, but last year it worked out okay, and again this year the on-paper gap is just too large to superstitiously pick someone else. But it’s easier to see how the Indians might lose to the Twins in 2018 than it was to compare them to the field in 2017. While it’s easy to overstate the impact of the Twins pitching additions (one could argue that Jake Odorozzi and Lance Lynn would be no more than #4 starters for the Tribe, even #5 if Danny Salazar could get it together), Cleveland’s bullpen is showing signs of vulnerability without a lot of clear candidates to step in, there are still injury questions surrounding Jason Kipnis and Michael Brantley, the outfield is unsettled...but it’s also sometimes easier to worry about these things as a fan. The Twins true quality for 2016-2017 might be matched by the win total, but the distribution was all off. A plexiglass principle year would not surprise. The Royals kept just enough of the band together to a) still be annoying and b) provide some measure of optimism for their partisans, but probably more of the former. I’ve been calling for the Tigers to dead cat bounce for a couple years; I’m surrendering and just expecting it for Miguel Cabrera. The White Sox have a lot of prospects and could well be the future of this division, but it’s still a year or two away.

AL WEST

1. Houston

2. Los Angeles

3. Seattle

4. Texas

5. Oakland

The Astros, in my crude system, are the second-best team in the AL...on offense and defense. Just slightly behind the Yankees and the Indians, respectively; combined, that’s enough to declare them the best and most well-rounded team on paper. Prior to Shohei Ohtani’s rough showing in spring training, I was set to pick the Angels as the second wildcard. Is dropping them a small sample size overreaction? Quite possibly, yes, but there wasn’t much separating teams like the Angels, Blue Jays, and Twins to begin with. You have to feel bad (unless you’re a fan of the…wait, do they even have a rival of note) for the Mariners - they now have the longest playoff drought in North American sports. Longer than the Cleveland Browns (this has been true for years but it is a miscarriage of justice that it’s not the Browns that hold this dubious distinction). They’ve been good enough to squeak out a second wildcard for a few years, but it never came together, and the window may be closing. The Rangers franchise history from 2010 - 2017 will make a fascinating case study some day, but I don’t think 2018 will add another dramatic return from the dead to the story. I still like the A’s players and think they could contend in the coming years, but the starting pitching is too shaky to predict good things this season.

NL EAST

1. Washington

2. New York

3. Philadelphia

4. Atlanta

5. Miami

The Nationals are basically what they have been for the last six years -- the clear favorite in the NL East. This is probably the last year for them to enjoy that status, but that’s a pretty impressive run in a division that features two big markets and a Braves franchise that until some point in the Washington run had basically contended for 25 years. As a neutral observer, it would be nice to at least see them get a NLCS out of the deal. Everyone talks about the health of the Mets rotation, but I think scoring runs might be a bigger question mark. I like the Phillies over the Braves this season, but over the next five years I’d flip that. Philly is a popular second wildcard pick--while that’s certainly within the realm of possibility, it will take better than forecast performances from some of the rookies (JP Crawford, Jorge Alfaro, Nick Williams) and Maikel Franko to make that happen. The Marlins are obviously a sad team to ponder, but the fact that Derek Jeter’s halo is being tarnished in the process makes it more entertaining than the usual Miami teardown.

NL CENTRAL

1. Chicago

2. St. Louis (wildcard)

3. Milwaukee

4. Pittsburgh

5. Cincinnati

The Cubs have the best offense in the NL by my estimation (although they distributed their runs across games so unfortunately last season that it wasn’t evident in the standings), their rotation is stronger entering this season (relative to last April) with the acquisitions of Jose Quintana and Yu Darvish, and I think they’re ready to re-challenge the Dodgers for NL superiority. The Cardinals look like a solid 86 win team, which is enough to make them a wildcard favorite; if they win with it, it’s a departure from the Pujols-era Cardinal teams which always had big stars, although maybe Carlos Martinez will take a step forward or Marcell Ozuna will hold his level and people will recognize how good he is outside of Miami and Stanton’s shadow. I look at four sources for team win projections when writing these up: my own crude version (fueled by the Steamer projections published at Fangraphs and some manual overrides on my part), Fangraphs, PECOTA from Baseball Prospectus, and Clay Davenport’s. The Brewers projected wins range from 76 - 86, which is tied with PECOTA darling Tampa Bay for the largest spread. Mine is on the low end of the spectrum--it just doesn’t seem like they have the pitching, and they have an outfield/corners logjam that’s good for depth but bad for allowing all of their name hitters to fully contribute. Last year I held on to hope for the Pirates; now I think it’s safe to say their 2012 - 2015 revival is over (come here for the bold statements). Amazingly, they would have been better off to have been in the NL East. If the only baseball I was allowed to watch this year was the games of one of the teams I picked last, I’d go with the Reds. Joey Votto, Luis Castillo, some interesting bullpen pieces, Billy Hamilton as a side show…it’s a fun team if not a good one.

NL WEST

1. Los Angeles

2. Arizona (wildcard)

3. San Francisco

4. Colorado

5. San Diego

I might be shortchanging the Dodgers by not picking them as the best team in the NL. They are still really good, they still have good depth, they still have the resources to address issues, but you know all that. There’s not much to say other than to tip one’s cap to the machine. I’m not bullish on the Diamondbacks, per se, but I’ll see your Zack Greinke decline concerns and raise you Zack Godley. I was surprised at how well the Giants came out when I put my forecast spreadsheet together; I was expecting 78-82 wins. A few more put them in prime wildcard contention position, but that was before Bumgarner and Shark became huge injury concerns. I don’t think the Rockies offense is all that good. I don’t think you can expect Charlie Blackmon to be as good, I still am skeptical of DJ LeMahieu, catcher and first base aren’t exactly settled. The Padres are definitely intriguing going forward, but it’s too soon to expect contention.

WORLD SERIES

Houston over Chicago

AL ROY: RF Austin Hays, BAL

AL Cy Young: Trevor Bauer, CLE

I don’t actually think this is the most likely outcome, I just love Trevor Bauer.

AL MVP: SS Carlos Correa, HOU

NL ROY: SP Alex Reyes, STL

NL Cy Young: Stephen Strasburg, WAS

NL MVP: RF Bryce Harper, WAS

## Tuesday, March 27, 2018

### 2018 Predictions

## Wednesday, February 28, 2018

### Enby Distribution, pt. 5: W% Estimate

While an earlier post contained the full explanation of the methodology used to estimate W%, it’s an important enough topic to repeat in full here. The methodology is not unique to Enby; it could be implemented with any estimate of the frequency of runs scored per game (and in fact I first implemented it with the Tango Distribution). As I discussed last time, the math may look complicated and require a computer to implement, but the model itself is arguably the simplest conceptually because it is based on the simple logic of how games are decided.

Let p(k) be the probability of scoring k runs in a game and q(m) be the probability of allowing m runs a game. If k is greater than m, then the team will win; if k is less than m, then the team will lose. If k and m are equal, then the game will go to extra innings. In setting it up this way, I am implicitly assuming that p(k) is the probability of scoring k runs in nine innings rather than in a game. This is not a horrible way to go about it since the average major league game has about 27 outs once the influences that cause shorter games (not batting in the ninth, rain) are balanced with the longer games created by extra innings. Still, it should be noted that the count of runs scored from a particular game does not necessarily arise from an equivalent opportunity context (as defined by innings or outs) of another game.

Given this notation, we can express the probability of winning a game in the standard nine innings as:

P(win 9) = p(1)*q(0) + p(2)*[q(0) +q(1)] +p(3)*[q(0) + q(1) + q(2)] + p(4)*[q(0) + q(1) + q(2) + q(3)] + ...

Extra innings will occur whenever k and m are equal:

P(X) = p(0)*q(0) + p(1)*q(1) + p(2)*q(2) + p(3)*q(3) + p(4)*q(4) + ...

When the game goes to extra innings, it becomes an inning by inning contest. Let n(k) be the probability of scoring k runs in an inning and r(m) be the probability of allowing m runs in an inning. If k is greater than m, the team wins; if k is less than m, the team loses; and if k is equal to m, then the process will repeat until a winner is determined.

To find the probability of each of the three possible outcomes of an extra inning, we can follow the same logic as used above for P(win 9). The probability of winning the inning is:

P(win inning) = n(1)*r(0) +n(2)*[r(0) +r(1)] +n(3)*[r(0) + r(1) + r(2)] + n(4)*[r(0) + r(1) + r(2) + r(3)] + ...

The probability of the game continuing (equivalent to tying the inning) is similar to P(extra innings above):

P(tie inning) = n(0)*r(0) + n(1)*r(1) +n(2)*r(2) + n(3)*r(3) + n(4)*r(4) + ...

The probability of winning in extra innings [P(win X)] is:

P(win X) = P(win inning) + P(tie inning)*P(win inning) + P(tie inning)^2*P(win inning) + P(tie inning)^3*P(win inning) + ...

This is a geometric series that simplifies to:

P(win X) = P(win inning)*[P(tie inning) + P(tie inning)^2 + P(tie inning)^3 + ...] = P(win inning)*1/[1 - P(tie inning)] = P(win inning)/[1 - P(tie inning)]

This could also be expressed in a very clever way using the Craps Principle if we had also computed P(lose inning); I did it that way last time, but it doesn’t really cut down on the amount of calculation necessary in this case.

Since I want these last few posts to serve as a comprehensive explanation of how to calculate the Enby run and win estimates, it is necessary to take a moment to review how to use the Tango Distribution to estimate the runs per inning distribution. c of course is the constant, set at .852 when looking with a head-to-head matchup. RI is runs/inning, which I’ve defined as RG/9:

a = c*RI^2

n(0) = RI/(RI + a)

d = 1 - c*f(0)

n(1) = (1 - n(0))*(1 - d)

n(k) = n(k - 1)*d for k >= 2

Once we have these three key probabilities [P(win 9), P(X), and P(win X)], the formula for W% is obvious:

W% = P(win 9) + P(X)*P(win X)

We will use the Enby Distribution to determine p(k) and q(m), and the Tango Distribution to determine n(k) and r(m). In both cases, we’ll use the Tango Distribution constant c = .852 since this works best when looking at a head-to-head matchup, which certainly is the applicable context when discussing W%.

I have put together a spreadsheet that will handle all of the calculations for you. The yellow cells are the ones that you can edit, with the most important being R (cell B1) and RA (cell L1), which naturally are where you enter the average R/G and RA/G for the team whose W% you’d like to estimate. The other yellow cell is for the c value of Tango Distribution. Please note that editing this cell will do nothing to change the Enby Distribution parameters--those are fixed based on using c = .852. Editing c in this cell (B8) will only change the estimates of the per inning scoring probabilities estimated by the Tango Distribution. I don’t advise changing this value, since .852 has been found to work best for head-to-head matchups and leaving it there keeps the Tango Distribution estimates consistent with the Enby Distribution estimates. The sheet also calculates Pythagenpat W% for a given exponent (which you can change in cell B15).

The calculator supports the same range of values as the one for single team run distribution introduced in part 9--RG at intervals of .25 between 0-3 and 7-15 runs, and at intervals of .05 between 3-7 runs. The vlookup function will round down to the next R/G value on the parameter sheet (for example, the two highest values supported are 14.75 and 15.00. You can enter 14.93 if you want, but the Enby calculation will be based on 14.75 (the Pythagenpat calculation will still be based on 14.93). Have some fun playing around with it, and next time we’ll look at how accurate the Enby estimate is compared to other W% models.

## Tuesday, February 13, 2018

### Doubles or Nothing

In previewing the season to come for any team, it is customary (for good reason) to start by taking a look back at the previous season. Sometimes this is a pleasant or at least unobjectionable experience. On some occasions, though, it forces one to review an absolute disaster of a season, as was turned in by the 2017 Ohio State Buckeyes.

OSU went 22-34, which was the lowest W% by a Buckeye club since 1974. Their 8-16 Big Ten record was the worst since 1987. The seven years in which Beals have been at the helm have produced a .564 W%, which excepting the largely overlapping span of 2008-2014, is the worst since 1986-1992. Beals has taken the program build by Bob Todd, who inherited the late 80s malaise, and driven it right back into mediocrity.

Yet merrily he rolls along, untroubled by the pressures of coaching at a school that fired its all-time winningest basketball coach for having two straight NCAA tournament misses, despite compiling a .500 record in Big Ten play over those two seasons. Beals and his unenlightened brand of baseball may be too small fry to draw the ire of AD Gene Smith, but tell that to the track, gymnastics, and women’s hockey coaches who have been pushed out in recent years. Beals record of doing less with a historically strong program is unmatched at the University.

When one peruses the likely lineup for 2018, it’s hard to think that a turnaround is imminent. Stranger things have happened, of course, but eight years into his tenure in Columbus, enough time to have nearly turned over two whole recruiting classes with no overlap, he is still plugging roster wholes with unproven JUCO transfers, failing to develop the high school recruits he’s brought in. It’s gotten to the point that if a player doesn’t find a role as a freshman, you can basically write him off as a future contributor.

Junior Jacob Barnwell is firmly ensconced at catcher; he was an average hitter last year and appears to have the coach seal of approval as a receiver, so he’s golden for playing time over the next two seasons. True freshman Dillon Dingler may be the heir apparent, with junior Andrew Fishel and redshirt freshman Scottie Seymour providing depth.

Seniors Bo Coolen and Noah McGowan, both JUCO transfers a year ago, will compete for first base; Coolen was bad offensively in 2017 with no power (.074 ISO), McGowan a little better but still below average. Junior Brady Cherry will move from the hot corner to the keystone, a curious move to this observer; Cherry flashed power as a freshman but was middling with the bat last year. That opens up third for sophomore Connor Pohl, who filled in admirably at second last year but does look more like a third baseman; on a rate basis he was the second most productive returning hitter, although it wasn’t a huge sample size (89 PA and it was very BA-heavy with a .325 BA/.225 SEC). JUCO transfer junior Kobie Foppe is penciled in at shortstop. The utility infielders are both sophomores; Noah West played more as a freshman, getting starts at second base (he didn’t hit at .213/.278/.303) and serving as a defensive replacement for Pohl, while Carpenter had 14 hitless (one walk) PAs. True freshman Aaron Hughes rounds out the roster.

Senior Tyler Cowles has the inside track at left field, coming off a first season as a JUCO transfer in which he hit .190/.309/.314 over 129 PA. McGowan could also contend for this spot, with backup outfield redshirt juniors Nate Romans and Ridge Winand also in the mix. JUCO transfer Malik Jones has been anointed as the centerfielder, with true freshman Jake Ruby as an understeady. Right field along with catcher is the only spot on the roster that features an established starter at the same position; sophomore Dominic Canzone is OSU’s best returning hitter, although it was BA heavy (.343 BA/.205 SEC). Some combination of Cowles, McGowan, and Fishel would appear to have the first crack at DH.

OSU’s pitching was an utter disaster last year, partly due to injury and partly because, well, Greg Beals. The only sure bet for the rotation appears to be senior Adam Niemeyer, with junior lefty Connor Curlis and senior Yianni Pavlopoulos (who closed as a sophomore) most likely to join him. Their RAs were 6.23, 5.03, and 7.65 respectively in 2017, although only Curlis had good health. Junior Ryan Feltner pitched poorly last year (7.32 RA over 62 IP despite 8.2 K/9), then went to the Cape Cod league and was named Reliever of the Year. Sophomore Jake Vance had a 6.92 RA over 26 innings, largely thanks to 20 walks, and is the fifth rotation candidate.

The perennial bright spot of the pitching staff is senior righty Seth Kinker, who easily led the team with 13 RAA over 58 innings, even getting 3 starts when everything fell to pieces. He figures to be the go-to reliever, with fifth-year senior righties Kyle Michalik, Austin Woody, and Curtiss Irving in middle relief. You’re not going to believe this, but their RAs ranged between 6.85 and 7.94 over a combined 66 innings. Sophomore Thomas Waning will follow Kinker and Michalik in one of Beals’ good traits, which is an affinity for sidearmers; Waning was effective (11 K, 4 W) in a 12 inning injury-shortened debut season. Junior Dustin Jourdan will be in the mix as well.

Beals also has an affinity for lefty specialists, which he will have to cultivate anew from sophomore Andrew Magno (4 appearances in 2016) and true freshman Luke Duermit, Griffan Smith, and Alex Theis.

The schedule is fairly typical, with the opening weekend (starting Friday) featuring a pair of games with both Canisus and UW-Milwaukee in Florida. The following weekend will see the Bucks in Arizona for the Big Ten/Pac-12 Challenge where they’ll play two each against Utah and Oregon State. Another trip to Florida to play low-level opponents (Nicholls State, Southern Miss, and Eastern Michigan) follows, followed by a trip to the Carolinas that will feature two games each against High Point, Coastal Carolina, and UNC-Wilmington.

Bizarrely, the home schedule opens March 16 with a weekend series against Cal St-Northridge; usually any home dates with non-Northern opponents come later in the calendar. Another non-conference weekend series against Georgetown follows, and then Big Ten play: Nebraska, @ Iowa, @ Penn St, Indiana, Minnesota, Illinois, Purdue, @ Michigan St. Mixed in will be a typically home-heavy mid-week slate (Eastern Michigan, Toledo, Kent St, Ohio University, Miami, Campbell) with road games at Ball St and Cincinnati.

As I wrote the roster outlook (which relied on my own knowledge and guesses but also heavily on the season preview released by the athletic department), two things that I already thought I knew struck me even more plainly.

1) This team does not appear to be very good. One can construct a rosy scenario where the pitching woes of 2017 were due largely to injury, but we’re talking about pitcher injuries. It takes extra tint on those glasses. It has to be better than last year, when nine pitchers started at least three games, but this team was 22-34; “better” isn’t going to cut it.

2) The offense has a couple solid returnees, but in the eighth year of Beals tenure, major positions on the diamond are still being papered over with JUCO transfers. There is no pipeline of young players getting their feet wet in utility roles and transitioning into starting as you would expect in a healthy program. There are no freshman studs to come in and commandeer lineup positions as you would expect in a strong program. It is quite easy to imagine a scenario in which five of the nine lineup spots are held by first or second-year JUCO transfers.

Beals has failed in recruiting, he has failed in player development, and most importantly he has failed to win at the level to which an OSU program should aspire. I’ve devoted many words in previous season previews and recaps (and the hashtag #BealsBall) to his asinine tactics. I won’t rehash that here, but I will end with a quote from the Meet the Team Dinner that program icon Nick Swisher was roped into headlining, which makes one seriously question in what decade Mr. Beals thinks he coaches:

*“Our goal in 2018 is to hit a lot of doubles,” said Beals on Saturday night.
*

## Monday, January 08, 2018

### Run Distribution and W%, 2017

I always start this post by looking at team records in blowout and non-blowout games. This year, after a Twitter discussion with Tom Tango, I’ve narrowed the definition of blowout to games in which the margin of victory is six runs or more (rather than five, the definition used by Baseball-Reference and that I had independently settled on). In 2017, the percentage of games decided by x runs and by >= x runs are:

If you draw the line at 5 runs, then 21.6% of games are classified as blowouts. At 6 runs, it drops to 15.3%. Tango asked his Twitter audience two different but related poll questions. The first was “what is the minimum margin that qualifies a game as a blowout?”, for which the plurality was six (39%, with 5, 7, and 8 the other options). The second was “what percentage of games do you consider to be blowouts?”, for which the plurality was 8-10% (43%, with the other choices being 4%-7%, 11%-15%, and 17-21%). Using the second criterion, one would have to set the bar at a margin of seven, at least in 2017.

As Tango pointed out, it is of interest that asking a similar question in different ways can produce different results. Of course this is well-known to anyone with a passing interest in public opinion polling. But here I want to focus more on some of the pros and cons of having a fixed standard for a blowout or one that varies depending on the actual empirical results from a given season.

A variable standard would recognize that as the run environment changes, the distribution of victory margin will surely change (independent of any concurrent changes in the distribution of team strength), expanding when runs are easier to come by. Of course, this point also means that what is a blowout in Coors Field may not be a blowout in Petco Park. The real determining factor of whether a game is a blowout is whether the probability that the trailing team can make a comeback (of course, picking one standard and applying to all games ignores the flow of a game; if you want to make a win probability-based definition, go for it).

On the other hand, a fixed standard allows the percentage of blowouts to vary over time, and maybe it should. If the majority of games were 1-0, it would sure feel like there were vary few blowouts even if the probability of the trailing team coming back was very low. Ideally, I would propose a mixed standard, in which the margin necessary for a blowout would not be a fixed % of games but rather somehow tied to the average runs scored/game. However, for the purpose of this post, Tango’s audience answering the simpler question is sufficient for my purposes. I never had any strong rationale for using five, and it does seem like 22% of games as blowouts is excessive.

Given the criterion that a blowout is a game in which the margin of victory was six or more, here are team records in non-blowouts:

Records in blowouts:

The difference between blowout and non-blowout records (B - N), and the percentage of games for each team that fall into those categories:

Keeping in mind that I changed definitions this year (and in so doing increased random variation if for no reason other than the smaller percentage of games in the blowout bucket), it is an oddity to see two of the very best teams in the game (HOU and WAS) with worse records in blowouts. Still, the general pattern is for strong teams to be even better in blowouts, per usual. San Diego stands out as the most extreme team, with an outlier poor record in blowouts offsetting an above-.500 record in non-blowouts, although given that they play in park with the lowest PF, their home/road discrepancy between blowout frequency should theoretically be higher than most teams.

A more interesting way to consider game-level results is to look at how teams perform when scoring or allowing a given number of runs. For the majors as a whole, here are the counts of games in which teams scored X runs:

The “marg” column shows the marginal W% for each additional run scored. In 2017, three was the mode of runs scored, while the second run resulted in the largest marginal increase in W%.

The major league average was 4.65 runs/game; at that level, here is the estimated probability of scoring x runs using the Enby Distribution (stopping at fifteen):

In graph form (again stopping at fifteen):

This is a pretty typical visual for the Enby fit to the major league average. It’s not perfect, but it is a reasonable model.

In previous years I’ve used this observed relationship to calculate metrics of team offense and defense based on the percentage of games in which they scored or allowed x runs. But I’ve always wanted to switch to using theoretical values based on the Enby Distribution, for a number of reasons:

1. The empirical distribution is subject to sample size fluctuations. In 2016, all 58 times that a team scored twelve runs in a game, they won; meanwhile, teams that scored thirteen runs were 46-1. Does that mean that scoring 12 runs is preferable to scoring 13 runs? Of course not--it's a quirk in the data. Additionally, the marginal values don’t necessary make sense even when W% increases from one runs scored level to another.

2. Using the empirical distribution forces one to use integer values for runs scored per game. Obviously the number of runs a team scores in a game is restricted to integer values, but not allowing theoretical fractional runs makes it very difficult to apply any sort of park adjustment to the team frequency of runs scored.

3. Related to #2 (really its root cause, although the park issue is important enough from the standpoint of using the results to evaluate teams that I wanted to single it out), when using the empirical data there is always a tradeoff that must be made between increasing the sample size and losing context. One could use multiple years of data to generate a smoother curve of marginal win probabilities, but in doing so one would lose centering at the season’s actual run scoring rate. On the other hand, one could split the data into AL and NL and more closely match context, but you would lose sample size and introduce more quirks into the data.

So this year I am able to use the Enby Distribution. I have Enby Distribution parameters at each interval of .05 runs/game. Since it takes a fair amount of manual work to calculate the Enby parameters, I have not done so at each .01 runs/game, and for this purpose it shouldn’t create too much distortion (more on this later). The first step is to take the major league average R/G (4.65) and park-adjust it. I could have park-adjusted home and road separately, and in theory you should be as granular as practical, but the data on teams scoring x runs or more is not readily available broken out between home and road. So each team’s standard PF which assumes a 50/50 split of home and road games is used. I then rounded this value to the nearest .05 and calculated the probability of scoring x runs using the Enby Distribution (with c = .852 since this exercise involves interactions between two teams).

For example, there were two teams that had PFs that produced a park-adjusted expected average of 4.90 R/G (ARI and TEX). In other words, an average offense playing half their games in Arizona's environment should have scored 4.90 runs/game; an average defense doing the same should have allowed 4.90 runs/game. The Enby distribution probabilities of scoring x runs for a team averaging 4.90 runs/game are:

For each x, it’s simple to estimate the probability of winning. If this team scores three runs in a particular game, then they will win if they allow 0 (4.3%), 1 (8.6%), or 2 runs (12.1%). As you can see, this construct assumes that their defense is league-average. If they allow three, then the game will go to extra innings, in which case they have a 50% chance of winning (this exercise doesn’t assume anything about inherent team quality), so in another 13.6% of games they win 50%. Thus, if this the Diamondbacks score three runs, they should win 31.8% of those games. If they allow three runs, it’s just the complement; they should win 68.2% of those games.

Using these probabilities and each team’s actual frequency of scoring x runs in 2017, I calculate what I call Game Offensive W% (gOW%) and Game Defensive W% (gDW%). It is analogous to James’ original construct of OW% except looking at the empirical distribution of runs scored rather than the average runs scored per game. (To avoid any confusion, James in 1986 also proposed constructing an OW% in the manner in which I calculate gOW%, which is where I got the idea).

As such, it is natural to compare the game versions of OW% and DW%, which consider a team’s run distribution, to their OW% and DW% figured using Pythagenpat in a traditional manner. Since I’m now using park-adjusted gOW%/gDW%, I have park-adjusted the standard versions as well. As a sample calculation, Detroit averaged 4.54 R/G and had a 1.02 PF, so their adjusted R/G is 4.45 (4.54/1.02). OW% The major league average was 4.65 R/G, and since they are assumed to have average defense we use that as their runs allowed. The Pythagenpat exponent is (4.45 + 4.65)^.29 = 1.90, and so their OW% is 4.45^1.90/(4.45^1.90 + 4.65^1.90) = .479, meaning that if the Tigers had average defense they would be estimated to win 47.9% of their games.

In previous year’s posts, the major league average gOW% and gDW% worked out to .500 by definition. Since this year I’m 1) using a theoretical run distribution from Enby 2) park-adjusting and 3) rounding team’s park-adjusted average runs to the nearest .05, it doesn’t work out perfectly. I did not fudge anything to correct for the league-level variation from .500, and the difference is small, but as a technical note do consider that the league average gOW% is .497 and the gDW% is .503.

For most teams, gOW% and OW% are very similar. Teams whose gOW% is higher than OW% distributed their runs more efficiently (at least to the extent that the methodology captures reality); the reverse is true for teams with gOW% lower than OW%. The teams that had differences of +/- 2 wins between the two metrics were (all of these are the g-type less the regular estimate, with the teams in descending order of absolute value of the difference):

Positive: SD, TOR

Negative: CHN, WAS, HOU, NYA, CLE

The Cubs had a standard OW% of .542, but a gOW% of .516, a difference of 4.3 wins which is the largest such discrepancy for any team offense/defense in the majors this year. I always like to pick out this team and present a graph of their runs scored frequencies to offer a visual explanation of what is going on, which is that they distributed their runs less efficiently for the purpose of winning games than would have been expected. The Cubs average 5.07 R/G, which I’ll round to 5.05 to be able to use an estimated distribution I have readily available from Enby (using the parameters for c = .767 in this case since we are just looking at one team in isolation):

The Cubs were shutout or held to one run in eight more games than one would expect for a team that average 5.05 R/G; of course, these are games that you almost certainly will not win. They scored three, four, or six runs significantly less than would be expected; while three and four are runs levels at which in 2017 you would expect to lose more often then you win, even scoring three runs makes a game winnable (.345 theoretical W% for a team in the Cubs’ run environment). The Cubs had 4.5 fewer games scoring between 9-12 runs than expected, which should be good from an efficiency perspective, since even at eight runs they should have had a .857 W%. But they more than offset that by scoring 13+ runs in a whopping 6.8% of their games, compared to an expectation of 2.0%--7.8 games more than expected where they gratuitously piled on runs. Chicago scored 13+ runs in 11 games, with Houston and Washington next with nine, and it’s no coincidence that they were also very inefficient offensively.

The preceding paragraph is an attempt to explain what happened; despite the choice of non-neutral wording, I’m not passing judgment. The question of whether run distribution is strongly predictive compared to average runs has not been studied in sufficient detail (by me at least), but I tend to think that the average is a reasonable indicator of quality going forward. Even if I’m wrong, it’s not “gratuitous” to continue to score runs after an arbitrary threshold with a higher probability of winning has been cleared. In some cases it may even be necessary, as the Cubs did have three games in which they allowed 13+ runs, although they weren’t the same games. As we saw earlier, major league teams were 111-0 when scoring 13+ runs, and 294-17 when scoring 10-12.

Teams with differences of +/- 2 wins between gDW% and standard DW%:

Positive: SD, CIN, NYN, MIN, TOR, DET

Negative: CLE, NYA

San Diego and Toronto had positive differences on both sides of the ball; the Yankees and Cleveland had negative difference for both. Thus it is no surprise that those teams show up on the list comparing gEW% to EW% (standard Pythagenpat). gEW% combines gOW% and gDW% indirectly by converting both to equivalent runs/game using Pythagenpat (see this post for the methodology):

Positive: SD, TOR, NYN, CIN, OAK

Negative: WAS, CHN, CLE, NYA, ARI, HOU

The Padres EW% was .362, but based on the manner in which they actually distributed their runs and runs allowed per game, one would have expected a .405 W%, a difference of 6.9 wins which is an enormous difference for these two approaches. In reality, they had a .438 W%, so Pythagenpat’s error was 12.3 wins which is enormous in its own right.

gEW% is usually (but not always!) a more accurate predictor of actual W% than EW%, which it should be since it has the benefit of additional information. However, gEW% assumes that runs scored and allowed are independent of each other on the game-level. Even if that were true theoretically (and given the existence of park factors alone it isn’t), gEW% would still be incapable of fully explaining discrepancies between actual records and Pythagenpat.

The various measures discussed are provided below for each team.

Finally, here are the Crude Team Ratings based on gEW% since I hadn’t yet calculated gEW% when that post was published: